FUNCTION: SfA2Sf - from SFA objects to SYMF objects

CALLING SEQUENCE:

SfA2Sf(sfa)

SfA2Sf(sfa, alist)

SFA[SfA2Sf](sfa)

SFA[SfA2Sf](sfa, alist)

PARAMETERS:

sf = any valid expression in SFA

alist = a list of alphabets

SYNOPSIS:

• The SfA2Sf function transforms any symmetric function of the SFA package into an object of SYMF for a given list of specific alphabets (by default A1).

• Valid bases for symmetric functions are 'e', 'h', 'p', 's', 'm'. Added bases and the c basis are not considered.

• Allowed alphabet expressions are linear combinations of formal alphabets A1, A2, A3, ..., for instance 3/2*A1 - A3 + 3/4 is valid.

• The inverse function is Sf2SfA.

• Whenever there is a conflict between the function name SfA2Sf and another name used in the same session, use the long form SFA['SfA2Sf'].

EXAMPLES:

> with(SFA):
> sfa := 7/5*s[2,2](2*A3) + s[3,1](A2)*p[2](A2) - q*e[2,1](A2):
> SfA2Sf(sfa);
 
                       7/5 s[2, 2] + s[3, 1] p2 - e2 e1 q
 
> SfA2Sf(sfa, [ A2, A3 ]);
 
                    7/5 s[2, 2](2 A3) + s[3, 1] p2 - e2 e1 q
 
> SfA2Sf(sfa, [ A2, 2*A3 ]);
 
                       7/5 s[2, 2] + s[3, 1] p2 - e2 e1 q